discrete mathematics is the mathematics of structures that come in separate, countable pieces — integers, truth values, finite sets, graphs — as opposed to the smooth continuum of analysis. 𐃏 no limits, no derivatives; instead: induction, counting, and exact structure. it is the native mathematics of computation — every data structure, algorithm, database query and cryptographic protocol below this page is discrete mathematics wearing a lab coat (Epp, Susanna S., 2019).
Proofs
logic is the study of valid inference: which conclusions are forced by which premises, independent of what the premises are about. 𐃏 it splits cleanly into a syntax (formulas, and rules for pushing them around) and a semantics (truth assignments, models), and the deepest theorems in the subject are exactly the ones that say when the two agree (Epp, Susanna S., 2019).